A364051 G.f. satisfies A(x) = 1 + x*A(x)^2 / (1 + x*A(x)^5).
1, 1, 1, -3, -21, -41, 166, 1460, 3445, -13503, -136721, -364412, 1285021, 14694643, 43144726, -132548857, -1709480698, -5456400119, 14285376285, 209281385564, 720201663662, -1572818128366, -26541960203077, -97918748134874, 173825501585400, 3453517916428141
Offset: 0
Keywords
Programs
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PARI
a(n) = if(n==0, 1, sum(k=0, n-1, (-1)^k*binomial(n, k)*binomial(2*n+3*k, n-1-k))/n);
Formula
a(n) = (1/n) * Sum_{k=0..n-1} (-1)^k * binomial(n,k) * binomial(2*n+3*k,n-1-k) for n > 0.